General Variational Expressions For The Calculation Of The Binding-Energies Of Anisotropic Donor States In Stepped Quantum-Wells

General variational expressions for the calculation of the binding energies of the low-lying bound states of an anisotropic donor in a quantum well (QW) are presented. To demonstrate the utilization of these expressions the binding energies of anisotropic donor states in a stepped quantum well are studied theoretically. The variations of the binding energies of the anisotropic donor states as a function of impurity position are presented for different values of the anisotropy factor gamma = m perpendicular-to*/m parallel-to*, where m perpendicular-to* and m parallel-to* represent the effective electron mass perpendicular to and parallel to the z axis (perpendicular to the interfaces of the QW), respectively. The peak position of the binding energy curves shifts to the deep side of the stepped well. The smaller the gamma, the larger the peak shift. The peak shift and the maximum in the binding energies are also dependent on the potential V2 of the step barrier. For the 2p0-like state the corresponding binding energy curve exhibits double peaks, different from the s- and 2p +/- -like states.